find the vertical shift of the sinusoidal function.

Explanation:

Step1: Recall vertical - shift formula

For a sinusoidal function of the form $y = A\sin(Bx - C)+D$ or $y = A\cos(Bx - C)+D$, the vertical shift is given by $D$. We can also find it by averaging the maximum and minimum values of the function.

Step2: Identify maximum and minimum values

From the graph, the maximum value of the function $f(x)$ is $y_{max}=2$ and the minimum value is $y_{min}=- 2$.

Step3: Calculate the vertical shift

The formula for the vertical shift $D=\frac{y_{max}+y_{min}}{2}$. Substitute $y_{max} = 2$ and $y_{min}=-2$ into the formula: $D=\frac{2+( - 2)}{2}=\frac{2 - 2}{2}=0$.

Answer:

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